TY - JOUR
T1 - On dimension stable spaces of measures
AU - Spector, Daniel
AU - Stolyarov, Dmitriy
N1 - Publisher Copyright:
© 2025 The Authors.
PY - 2026/3
Y1 - 2026/3
N2 - In this paper, we define spaces of measures D S β ( R d ) with dimensional stability β ∈ ( 0 , d ) . These spaces bridge between M b ( R d ) , the space of finite Radon measures, and D S d ( R d ) = H 1 ( R d ) , the real Hardy space. We show the spaces D S β ( R d ) support Sobolev inequalities for β ∈ ( 0 , d ] , while for any β ∈ [ 0 , d ] we show that the lower Hausdorff dimension of an element of D S β ( R d ) is at least β .
AB - In this paper, we define spaces of measures D S β ( R d ) with dimensional stability β ∈ ( 0 , d ) . These spaces bridge between M b ( R d ) , the space of finite Radon measures, and D S d ( R d ) = H 1 ( R d ) , the real Hardy space. We show the spaces D S β ( R d ) support Sobolev inequalities for β ∈ ( 0 , d ] , while for any β ∈ [ 0 , d ] we show that the lower Hausdorff dimension of an element of D S β ( R d ) is at least β .
KW - Atomic decomposition
KW - Fractional maximal functions
KW - Hausdorff content
KW - Hausdorff dimension
KW - L Sobolev inequalities
KW - Riesz potentials
UR - https://www.scopus.com/pages/publications/105021090394
UR - https://www.scopus.com/pages/publications/105021090394#tab=citedBy
U2 - 10.1016/j.na.2025.113997
DO - 10.1016/j.na.2025.113997
M3 - Article
AN - SCOPUS:105021090394
SN - 0362-546X
VL - 264
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
M1 - 113997
ER -